Covariate Data and Movement Timing
Markus Min
2023-03-27
Objectives
- Assess concerns over data availability.
- Investigate multicollinearity between our three continuous covariates: flow, spill, and temperature.
- Look at passage timing, to determine when covariate data will be most useful.
- Decide how covariate data will be matched to state occupancy (e.g., a window approach)
Matching covariate data to state occupancy
Example of movements for one fish:
## state date_time pathway
## 2223 mainstem, BON to MCN 2014-08-16 11:53:22 BON (adult)
## 2224 mainstem, MCN to ICH or PRA 2014-09-20 05:23:09 MCN (adult)
## 2225 mainstem, PRA to RIS 2014-09-24 05:30:10 PRA (adult)
## 2226 mainstem, RIS to RRE 2014-09-29 07:00:14 implicit
## 2227 mainstem, RRE to WEL 2014-09-29 07:00:14 RRE (adult)
## 2228 mainstem, upstream of WEL 2014-10-03 08:05:33 WEL (adult)
## 2229 Methow River Upstream 2014-10-20 05:52:58 MET_upstream
## 2230 mainstem, upstream of WEL 2014-11-13 10:17:14 implicit
## 2231 mainstem, RRE to WEL 2014-11-13 10:17:14 implicit
## 2232 mainstem, RIS to RRE 2014-11-13 10:17:14 implicit
## 2233 mainstem, PRA to RIS 2014-11-13 10:17:14 implicit
## 2234 mainstem, MCN to ICH or PRA 2014-11-13 10:17:14 implicit
## 2235 mainstem, ICH to LGR 2014-11-13 10:17:14 ICH (adult)
## 2236 mainstem, upstream of LGR 2014-11-26 13:54:45 LGR (adult)
## 2237 Salmon River 2015-03-28 01:19:45 SAL_sitesCovariate Data
Summary
- The following dams lack winter (November - Feburary) temperature data: Bonneville, Rock Island (until 2012), Rocky Reach (until 2012), Wells Dam (until 2013)
- Spill data can be a bit patchy - are missing spill values zeros?
- Spill and flow are strongly correlated; VIF vary, but are between 2 and 8. R^2 values range 0.55 - 0.9
- In some years, spill appears to follow the relationship spill = flow - X, but the value of X changes from year to year. This appears to be especially true for the four Snake River Dams
Bonneville Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 3607 3425Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -92.339 -22.198 -6.513 20.017 87.547
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -58.580290 1.058786 -55.33 <2e-16 ***
## flow 0.581807 0.005398 107.79 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 36.62 on 7030 degrees of freedom
## (273 observations deleted due to missingness)
## Multiple R-squared: 0.623, Adjusted R-squared: 0.623
## F-statistic: 1.162e+04 on 1 and 7030 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.737 -3.851 1.940 4.272 7.149
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.799147 0.231904 85.38 <2e-16 ***
## flow -0.021936 0.001043 -21.02 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.173 on 3423 degrees of freedom
## (3880 observations deleted due to missingness)
## Multiple R-squared: 0.1144, Adjusted R-squared: 0.1141
## F-statistic: 442 on 1 and 3423 DF, p-value: < 2.2e-16
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -88.259 -37.269 7.213 24.494 200.329
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 60.7130 2.6640 22.790 < 2e-16 ***
## temp 1.2691 0.1639 7.741 1.29e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 52.72 on 3423 degrees of freedom
## (3880 observations deleted due to missingness)
## Multiple R-squared: 0.01721, Adjusted R-squared: 0.01692
## F-statistic: 59.92 on 1 and 3423 DF, p-value: 1.289e-14Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.129121 1.129121
##
## [[2]]
## flow spill
## 2.1435 2.1435
##
## [[3]]
## spill temp
## 1.017506 1.017506John Day Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 448 6584Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -90.623 -14.601 -0.062 16.228 92.384
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -56.161515 0.671859 -83.59 <2e-16 ***
## flow 0.534644 0.003576 149.50 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 24.62 on 7030 degrees of freedom
## (273 observations deleted due to missingness)
## Multiple R-squared: 0.7607, Adjusted R-squared: 0.7607
## F-statistic: 2.235e+04 on 1 and 7030 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.5939 -6.1873 0.3332 5.9630 10.5648
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.2905210 0.1790238 74.239 <2e-16 ***
## flow -0.0043790 0.0009367 -4.675 3e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.371 on 6582 degrees of freedom
## (721 observations deleted due to missingness)
## Multiple R-squared: 0.00331, Adjusted R-squared: 0.003158
## F-statistic: 21.86 on 1 and 6582 DF, p-value: 2.998e-06
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -55.08 -28.91 -19.88 17.34 247.57
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.29933 1.35100 9.104 <2e-16 ***
## temp 1.92895 0.09603 20.087 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 49.72 on 6582 degrees of freedom
## (721 observations deleted due to missingness)
## Multiple R-squared: 0.05776, Adjusted R-squared: 0.05762
## F-statistic: 403.5 on 1 and 6582 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.003321 1.003321
##
## [[2]]
## flow spill
## 4.219045 4.219045
##
## [[3]]
## spill temp
## 1.061299 1.061299The Dalles Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 280 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 434 6591Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -101.903 -16.900 0.344 20.779 126.049
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -60.435506 0.778870 -77.59 <2e-16 ***
## flow 0.582702 0.004264 136.66 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27.74 on 7023 degrees of freedom
## (280 observations deleted due to missingness)
## Multiple R-squared: 0.7267, Adjusted R-squared: 0.7267
## F-statistic: 1.868e+04 on 1 and 7023 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.4977 -6.1205 0.3951 5.8010 10.4654
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.6825394 0.1810168 75.587 < 2e-16 ***
## flow -0.0066120 0.0009764 -6.772 1.38e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.286 on 6589 degrees of freedom
## (714 observations deleted due to missingness)
## Multiple R-squared: 0.006911, Adjusted R-squared: 0.00676
## F-statistic: 45.85 on 1 and 6589 DF, p-value: 1.384e-11
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -62.61 -28.65 -17.73 21.11 272.82
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.596 1.421 5.347 9.26e-08 ***
## temp 2.441 0.101 24.168 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 51.71 on 6589 degrees of freedom
## (714 observations deleted due to missingness)
## Multiple R-squared: 0.08143, Adjusted R-squared: 0.08129
## F-statistic: 584.1 on 1 and 6589 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.006959 1.006959
##
## [[2]]
## flow spill
## 3.718405 3.718405
##
## [[3]]
## spill temp
## 1.088647 1.088647McNary Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 13 7019Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -95.607 -19.844 -1.294 20.349 91.304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -84.513785 0.849167 -99.53 <2e-16 ***
## flow 0.792072 0.004517 175.35 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 30.62 on 7030 degrees of freedom
## (273 observations deleted due to missingness)
## Multiple R-squared: 0.8139, Adjusted R-squared: 0.8139
## F-statistic: 3.075e+04 on 1 and 7030 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.1274 -6.0829 -0.1466 5.9885 17.3149
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.9762940 0.1735677 69.001 <2e-16 ***
## flow -0.0004554 0.0009228 -0.494 0.622
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.252 on 7017 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 3.471e-05, Adjusted R-squared: -0.0001078
## F-statistic: 0.2436 on 1 and 7017 DF, p-value: 0.6217
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -104.44 -42.03 -24.10 26.84 317.75
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.6647 1.7519 7.229 5.37e-13 ***
## temp 3.1375 0.1303 24.072 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 68.26 on 7017 degrees of freedom
## (286 observations deleted due to missingness)
## Multiple R-squared: 0.07628, Adjusted R-squared: 0.07615
## F-statistic: 579.5 on 1 and 7017 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.000035 1.000035
##
## [[2]]
## flow spill
## 5.373753 5.373753
##
## [[3]]
## spill temp
## 1.082582 1.082582Priest Rapids Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 965 6067Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -55.491 -14.096 -0.015 11.494 87.417
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -51.993141 0.629370 -82.61 <2e-16 ***
## flow 0.620771 0.004882 127.15 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.86 on 7030 degrees of freedom
## (273 observations deleted due to missingness)
## Multiple R-squared: 0.6969, Adjusted R-squared: 0.6969
## F-statistic: 1.617e+04 on 1 and 7030 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.0637 -5.5323 0.2589 5.5389 9.4832
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.189562 0.185454 65.728 < 2e-16 ***
## flow -0.006472 0.001400 -4.623 3.85e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.747 on 6065 degrees of freedom
## (1238 observations deleted due to missingness)
## Multiple R-squared: 0.003512, Adjusted R-squared: 0.003348
## F-statistic: 21.38 on 1 and 6065 DF, p-value: 3.852e-06
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32.366 -20.686 -15.321 1.104 218.354
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.17874 1.10912 10.98 <2e-16 ***
## temp 1.01487 0.08683 11.69 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 38.93 on 6065 degrees of freedom
## (1238 observations deleted due to missingness)
## Multiple R-squared: 0.02203, Adjusted R-squared: 0.02187
## F-statistic: 136.6 on 1 and 6065 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.003525 1.003525
##
## [[2]]
## flow spill
## 3.416603 3.416603
##
## [[3]]
## spill temp
## 1.022524 1.022524Rock Island Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 1241 5791Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.512 -8.407 -0.435 7.186 122.675
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -29.602166 0.438001 -67.58 <2e-16 ***
## flow 0.365947 0.003557 102.88 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.93 on 7030 degrees of freedom
## (273 observations deleted due to missingness)
## Multiple R-squared: 0.6009, Adjusted R-squared: 0.6008
## F-statistic: 1.058e+04 on 1 and 7030 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.338 -5.246 1.327 5.159 10.651
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14.064049 0.194409 72.34 <2e-16 ***
## flow -0.017153 0.001515 -11.33 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.588 on 5789 degrees of freedom
## (1514 observations deleted due to missingness)
## Multiple R-squared: 0.02168, Adjusted R-squared: 0.02151
## F-statistic: 128.3 on 1 and 5789 DF, p-value: < 2.2e-16
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.502 -14.556 -10.353 7.457 193.300
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.11902 0.72238 12.624 <2e-16 ***
## temp 0.45548 0.05437 8.377 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.37 on 5789 degrees of freedom
## (1514 observations deleted due to missingness)
## Multiple R-squared: 0.01198, Adjusted R-squared: 0.01181
## F-statistic: 70.18 on 1 and 5789 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.022158 1.022158
##
## [[2]]
## flow spill
## 2.594388 2.594388
##
## [[3]]
## spill temp
## 1.012123 1.012123Rocky Reach Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 1259 5773Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -38.089 -7.864 -0.540 6.408 115.994
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -30.537689 0.400374 -76.27 <2e-16 ***
## flow 0.352975 0.003356 105.19 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.97 on 7030 degrees of freedom
## (273 observations deleted due to missingness)
## Multiple R-squared: 0.6115, Adjusted R-squared: 0.6114
## F-statistic: 1.106e+04 on 1 and 7030 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.282 -5.296 1.545 5.149 8.098
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14.22148 0.19036 74.71 <2e-16 ***
## flow -0.01707 0.00153 -11.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.579 on 5771 degrees of freedom
## (1532 observations deleted due to missingness)
## Multiple R-squared: 0.02112, Adjusted R-squared: 0.02095
## F-statistic: 124.5 on 1 and 5771 DF, p-value: < 2.2e-16
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.704 -10.101 -9.334 0.143 194.634
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.00495 0.71098 12.665 <2e-16 ***
## temp 0.08313 0.05268 1.578 0.115
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.57 on 5771 degrees of freedom
## (1532 observations deleted due to missingness)
## Multiple R-squared: 0.0004312, Adjusted R-squared: 0.000258
## F-statistic: 2.49 on 1 and 5771 DF, p-value: 0.1146Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.021572 1.021572
##
## [[2]]
## flow spill
## 2.732757 2.732757
##
## [[3]]
## spill temp
## 1.000431 1.000431Wells Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 8 1904 5120Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.809 -7.107 -0.581 5.817 102.561
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -29.292950 0.362110 -80.89 <2e-16 ***
## flow 0.344634 0.003029 113.79 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.63 on 7022 degrees of freedom
## (281 observations deleted due to missingness)
## Multiple R-squared: 0.6484, Adjusted R-squared: 0.6483
## F-statistic: 1.295e+04 on 1 and 7022 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.477 -5.130 1.119 5.220 8.722
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 13.489958 0.199053 67.771 <2e-16 ***
## flow -0.014769 0.001569 -9.414 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.52 on 5126 degrees of freedom
## (2177 observations deleted due to missingness)
## Multiple R-squared: 0.017, Adjusted R-squared: 0.0168
## F-statistic: 88.63 on 1 and 5126 DF, p-value: < 2.2e-16
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.127 -11.292 -5.974 -1.496 173.559
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.69962 0.72078 14.844 <2e-16 ***
## temp 0.07081 0.05536 1.279 0.201
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.06 on 5118 degrees of freedom
## (2185 observations deleted due to missingness)
## Multiple R-squared: 0.0003196, Adjusted R-squared: 0.0001243
## F-statistic: 1.636 on 1 and 5118 DF, p-value: 0.2009Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.018223 1.018223
##
## [[2]]
## flow spill
## 3.130486 3.130486
##
## [[3]]
## spill temp
## 1.00032 1.00032Ice Harbor Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 15 7017Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.649 -6.195 -0.357 8.586 38.600
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -13.724519 0.227780 -60.25 <2e-16 ***
## flow 0.689502 0.003906 176.52 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.87 on 7030 degrees of freedom
## (273 observations deleted due to missingness)
## Multiple R-squared: 0.8159, Adjusted R-squared: 0.8159
## F-statistic: 3.116e+04 on 1 and 7030 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.6940 -6.2951 0.2389 5.8858 10.6578
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.348746 0.123392 100.078 < 2e-16 ***
## flow -0.007396 0.002115 -3.497 0.000473 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.42 on 7015 degrees of freedom
## (288 observations deleted due to missingness)
## Multiple R-squared: 0.00174, Adjusted R-squared: 0.001598
## F-statistic: 12.23 on 1 and 7015 DF, p-value: 0.0004731
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.431 -15.915 -12.082 6.604 140.958
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.60196 0.69138 13.89 <2e-16 ***
## temp 0.68310 0.05076 13.46 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 27.32 on 7015 degrees of freedom
## (288 observations deleted due to missingness)
## Multiple R-squared: 0.02517, Adjusted R-squared: 0.02503
## F-statistic: 181.1 on 1 and 7015 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.001743 1.001743
##
## [[2]]
## flow spill
## 5.425536 5.425536
##
## [[3]]
## spill temp
## 1.025818 1.025818Lower Monumental Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 280 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 461 6564Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.056 -4.884 -1.055 5.794 61.922
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.348479 0.201406 -36.49 <2e-16 ***
## flow 0.407361 0.003545 114.92 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.39 on 7023 degrees of freedom
## (280 observations deleted due to missingness)
## Multiple R-squared: 0.6528, Adjusted R-squared: 0.6528
## F-statistic: 1.321e+04 on 1 and 7023 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.493 -6.154 0.397 5.777 9.999
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.54669 0.12457 100.717 < 2e-16 ***
## flow -0.01139 0.00214 -5.325 1.04e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.185 on 6562 degrees of freedom
## (741 observations deleted due to missingness)
## Multiple R-squared: 0.004303, Adjusted R-squared: 0.004151
## F-statistic: 28.36 on 1 and 6562 DF, p-value: 1.043e-07
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.928 -10.226 -7.655 3.084 126.833
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.07526 0.47818 12.71 <2e-16 ***
## temp 0.46397 0.03535 13.12 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.75 on 6562 degrees of freedom
## (741 observations deleted due to missingness)
## Multiple R-squared: 0.02558, Adjusted R-squared: 0.02543
## F-statistic: 172.2 on 1 and 6562 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.004321 1.004321
##
## [[2]]
## flow spill
## 2.870193 2.870193
##
## [[3]]
## spill temp
## 1.026247 1.026247Little Goose Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 280 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 454 6571Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39.082 -3.093 0.254 3.232 110.353
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.176430 0.180752 -50.77 <2e-16 ***
## flow 0.432874 0.003262 132.72 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.341 on 7023 degrees of freedom
## (280 observations deleted due to missingness)
## Multiple R-squared: 0.7149, Adjusted R-squared: 0.7149
## F-statistic: 1.761e+04 on 1 and 7023 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.0070 -6.0127 0.0896 5.9639 10.1816
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.041892 0.122645 98.185 <2e-16 ***
## flow -0.005539 0.002158 -2.566 0.0103 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.102 on 6569 degrees of freedom
## (734 observations deleted due to missingness)
## Multiple R-squared: 0.001002, Adjusted R-squared: 0.0008496
## F-statistic: 6.586 on 1 and 6569 DF, p-value: 0.0103
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.849 -9.238 -7.103 2.647 172.191
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.75320 0.47600 12.09 <2e-16 ***
## temp 0.39236 0.03584 10.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.74 on 6569 degrees of freedom
## (734 observations deleted due to missingness)
## Multiple R-squared: 0.01791, Adjusted R-squared: 0.01776
## F-statistic: 119.8 on 1 and 6569 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.001003 1.001003
##
## [[2]]
## flow spill
## 3.504784 3.504784
##
## [[3]]
## spill temp
## 1.018239 1.018239Lower Granite Dam
Data availability
Availability of spill/temperature/flow data, by number of days (2004-present):
##
## none spill flow temp
## 273 0 0 0
## spill + temp temp + flow spill + flow spill + temp + flow
## 0 0 14 7018Data by day of year
## [[1]]
##
## [[2]]
##
## [[3]]
Regressions and VIF
## [[1]]
##
## [[2]]
##
## Call:
## lm(formula = spill ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -37.194 -4.509 -0.893 4.765 51.799
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.984336 0.182926 -43.65 <2e-16 ***
## flow 0.421640 0.003195 131.97 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.474 on 7030 degrees of freedom
## (273 observations deleted due to missingness)
## Multiple R-squared: 0.7124, Adjusted R-squared: 0.7124
## F-statistic: 1.742e+04 on 1 and 7030 DF, p-value: < 2.2e-16
##
##
## [[3]]
##
## [[4]]
##
## Call:
## lm(formula = temp ~ flow, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.9040 -5.8980 -0.4319 6.3122 10.3850
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.014712 0.114800 95.947 <2e-16 ***
## flow 0.001431 0.002007 0.713 0.476
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.933 on 7016 degrees of freedom
## (287 observations deleted due to missingness)
## Multiple R-squared: 7.241e-05, Adjusted R-squared: -7.011e-05
## F-statistic: 0.5081 on 1 and 7016 DF, p-value: 0.476
##
##
## [[5]]
##
## [[6]]
##
## Call:
## lm(formula = spill ~ temp, data = cont_cov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.138 -8.931 -6.075 2.895 116.193
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.65041 0.43463 8.399 <2e-16 ***
## temp 0.66313 0.03458 19.175 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.19 on 7016 degrees of freedom
## (287 observations deleted due to missingness)
## Multiple R-squared: 0.04979, Adjusted R-squared: 0.04966
## F-statistic: 367.7 on 1 and 7016 DF, p-value: < 2.2e-16Variance inflation factors (Spill, Temperature, and Flow):
## [[1]]
## flow temp
## 1.000072 1.000072
##
## [[2]]
## flow spill
## 3.458132 3.458132
##
## [[3]]
## spill temp
## 1.052403 1.052403State timing
Dam ascents
Tributary entries
